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Canonical Analysis of Brans-Dicke Theory Addresses Hamiltonian Inequivalence between Jordan and Einstein Frames
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Jordan and Einstein frame are studied under the light of Hamiltonian formalism. Dirac's constraint theory for Hamiltonian systems is applied to Brans-Dicke theory in the Jordan Frame. In both Jordan and Einstein frame, Brans-Dicke theory has four secondary first class constraints and their constraint algebra is closed. We show, contrary to what is generally believed, the Weyl (conformal) transformation, between the two frames, is not a canonical transformation, in the sense of Hamiltonian formalism. This addresses quantum mechanical inequivalence as well. A canonical transformation is shown.
Forward citations
Cited by 2 Pith papers
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Canonical Clock Sectors and Relational Frame Equivalence in Brans--Dicke Theory
Apparent Jordan–Einstein inequivalence after relational deparametrization is a clock-sector mismatch; a frame-adapted canonical chart restores identical reduced Hamiltonians.
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Aspects of Geometrodynamics in the Jordan and Einstein Frames
The Jordan and Einstein frames are connected by a Hamiltonian canonical transformation only after gauge-fixing lapse and shift, and this maps the FJNW naked singularity to the BBMB black hole.
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